{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optional Lab: Model Representation\n",
    "\n",
    "<figure>\n",
    " <img src=\"./images/C1_W1_L3_S1_Lecture_b.png\"   style=\"width:600px;height:200px;\">\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goals\n",
    "In this lab you will:\n",
    "- Learn to implement the model $f_{w,b}$ for linear regression with one variable"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "7fd3fbe6",
   "metadata": {},
   "source": [
    "## Notation\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tools\n",
    "In this lab you will make use of: \n",
    "- NumPy, a popular library for scientific computing\n",
    "- Matplotlib, a popular library for plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Statement\n",
    "<img align=\"left\" src=\"./images/C1_W1_L3_S1_trainingdata.png\"    style=\" width:380px; padding: 10px;  \" /> \n",
    "\n",
    "As in the lecture, you will use the motivating example of housing price prediction.  \n",
    "This lab will use a simple data set with only two data points - a house with 1000 square feet(sqft) sold for \\\\$300,000 and a house with 2000 square feet sold for \\\\$500,000. These two points will constitute our *data or training set*. In this lab, the units of size are 1000 sqft and the units of price are 1000s of dollars.\n",
    "\n",
    "| Size (1000 sqft)     | Price (1000s of dollars) |\n",
    "| -------------------| ------------------------ |\n",
    "| 1.0               | 300                      |\n",
    "| 2.0               | 500                      |\n",
    "\n",
    "You would like to fit a linear regression model (shown above as the blue straight line) through these two points, so you can then predict price for other houses - say, a house with 1200 sqft.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please run the following code cell to create your `x_train` and `y_train` variables. The data is stored in one-dimensional NumPy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train = [1. 2.]\n",
      "y_train = [300. 500.]\n"
     ]
    }
   ],
   "source": [
    "# x_train is the input variable (size in 1000 square feet)\n",
    "# y_train is the target (price in 1000s of dollars)\n",
    "x_train = np.array([1.0, 2.0])\n",
    "y_train = np.array([300.0, 500.0])\n",
    "print(f\"x_train = {x_train}\")\n",
    "print(f\"y_train = {y_train}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">**Note**: The course will frequently utilize the python 'f-string' output formatting described [here](https://docs.python.org/3/tutorial/inputoutput.html) when printing. The content between the curly braces is evaluated when producing the output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Number of training examples `m`\n",
    "You will use `m` to denote the number of training examples. Numpy arrays have a `.shape` parameter. `x_train.shape` returns a python tuple with an entry for each dimension. `x_train.shape[0]` is the length of the array and number of examples as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train.shape: (2,)\n",
      "Number of training examples is: 2\n"
     ]
    }
   ],
   "source": [
    "# m is the number of training examples\n",
    "print(f\"x_train.shape: {x_train.shape}\")\n",
    "m = x_train.shape[0]\n",
    "print(f\"Number of training examples is: {m}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can also use the Python `len()` function as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training examples is: 2\n"
     ]
    }
   ],
   "source": [
    "# m is the number of training examples\n",
    "m = len(x_train)\n",
    "print(f\"Number of training examples is: {m}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training example `x_i, y_i`\n",
    "\n",
    "You will use ($x^{(i)}$, $y^{(i)}$) to denote the $i^{th}$ training example. Since Python is zero indexed, ($x^{(0)}$, $y^{(0)}$) is (1.0, 300.0) and ($x^{(1)}$, $y^{(1)}$) is (2.0, 500.0).\n",
    "\n",
    "To access a value in a Numpy array, one indexes the array with the desired offset. For example the syntax to access location zero of `x_train` is `x_train[0]`.\n",
    "Run the next code block below to get the $i^{th}$ training example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x^(1), y^(1)) = (2.0, 500.0)\n"
     ]
    }
   ],
   "source": [
    "i = 1 # Change this to 1 to see (x^1, y^1)\n",
    "\n",
    "x_i = x_train[i]\n",
    "y_i = y_train[i]\n",
    "print(f\"(x^({i}), y^({i})) = ({x_i}, {y_i})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can plot these two points using the `scatter()` function in the `matplotlib` library, as shown in the cell below. \n",
    "- The function arguments `marker` and `x` show the points as red crosses (the default is blue dots).\n",
    "\n",
    "You can use other functions in the `matplotlib` library to set the title and labels to display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, y_train, marker='o', color='red')\n",
    "plt.xlabel('Size in 1000 square feet')\n",
    "plt.ylabel('Price in 1000s of dollars')\n",
    "plt.grid(True)\n",
    "plt.title('Training Data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model function\n",
    "\n",
    "As described in lecture, the model function for linear regression (which is a function that maps from `x` to `y`) is represented as \n",
    "\n",
    "$$ f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{1}$$\n",
    "\n",
    "The formula above is how you can represent straight lines - different values of $w$ and $b$ give you different straight lines on the plot. <br/> <br/> <br/> <br/> <br/> \n",
    "\n",
    "Let's try to get a better intuition for this through the code blocks below. Let's start with $w = 100$ and $b = 100$. \n",
    "\n",
    "**Note: You can come back to this cell to adjust the model's w and b parameters**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w: 200\n",
      "b: 100\n"
     ]
    }
   ],
   "source": [
    "w = 200\n",
    "b = 100\n",
    "print(f\"w: {w}\")\n",
    "print(f\"b: {b}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's compute the value of $f_{w,b}(x^{(i)})$ for your two data points. You can explicitly write this out for each data point as - \n",
    "\n",
    "for $x^{(0)}$, `f_wb = w * x[0] + b`\n",
    "\n",
    "for $x^{(1)}$, `f_wb = w * x[1] + b`\n",
    "\n",
    "For a large number of data points, this can get unwieldy and repetitive. So instead, you can calculate the function output in a `for` loop as shown in the `compute_model_output` function below.\n",
    "> **Note**: The argument description `(ndarray (m,))` describes a Numpy n-dimensional array of shape (m,). `(scalar)` describes an argument without dimensions, just a magnitude.  \n",
    "> **Note**: `np.zero(n)` will return a one-dimensional numpy array with $n$ entries   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_model_output(x, w, b):\n",
    "    \"\"\"\n",
    "    Computes the prediction of a linear model\n",
    "    Args:\n",
    "      x (ndarray (m,)): Data, m examples \n",
    "      w,b (scalar)    : model parameters  \n",
    "    Returns\n",
    "      f_wb (ndarray (m,)): model prediction\n",
    "    \"\"\"\n",
    "    m = x.shape[0]\n",
    "    f_wb = np.zeros(m)\n",
    "    for i in range(m):\n",
    "        f_wb[i] = w * x[i] + b\n",
    "\n",
    "    return f_wb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's call the `compute_model_output` function and plot the output.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_wb = compute_model_output(x_train, w, b)\n",
    "\n",
    "plt.plot(x_train, f_wb, color='blue', label='Linear model')\n",
    "plt.scatter(x_train, y_train, color='red', marker='o')\n",
    "plt.title('Linear regression')\n",
    "plt.xlabel('Size in 1000 square feet')\n",
    "plt.ylabel('Price in 1000s of dollars')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, setting $w = 100$ and $b = 100$ does *not* result in a line that fits our data. \n",
    "\n",
    "### Challenge\n",
    "Try experimenting with different values of $w$ and $b$. What should the values be for a line that fits our data?\n",
    "\n",
    "#### Tip:\n",
    "You can use your mouse to click on the green \"Hints\" below to reveal some hints for choosing b and w."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary>\n",
    "    <font size='3', color='darkgreen'><b>Hints</b></font>\n",
    "</summary>\n",
    "    <p>\n",
    "    <ul>\n",
    "        <li>Try $w = 200$ and $b = 100$ </li>\n",
    "    </ul>\n",
    "    </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction\n",
    "Now that we have a model, we can use it to make our original prediction. Let's predict the price of a house with 1200 sqft. Since the units of $x$ are in 1000's of sqft, $x$ is 1.2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$340 thousand dollars\n"
     ]
    }
   ],
   "source": [
    "w = 200                         \n",
    "b = 100    \n",
    "x_i = 1.2\n",
    "cost_1200sqft = w * x_i + b    \n",
    "\n",
    "print(f\"${cost_1200sqft:.0f} thousand dollars\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Congratulations!\n",
    "In this lab you have learned:\n",
    " - Linear regression builds a model which establishes a relationship between features and targets\n",
    "     - In the example above, the feature was house size and the target was house price\n",
    "     - for simple linear regression, the model has two parameters $w$ and $b$ whose values are 'fit' using *training data*.\n",
    "     - once a model's parameters have been determined, the model can be used to make predictions on novel data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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